Answer:
120 cards
Step-by-step explanation:
2,3,4,5, and 6 are all factors of 120
Answer:
x = 2,94 ft
h = 0,88 ft
C(min) = 12,23 $
Step-by-step explanation:
Let x be radius of the base and h th hight of th cylinder then
Area of the bottom A₁ = π*x²
And cost of the bottom C₁ = 0,15*π*x²
Lateral area A₂
A₂ = 2*π*x*h but V = 24 ft³ V = π*x²*h h = V/ π*x²
A₂ = 2*π*x* (24/ π*x²)
A₂ = 48 /x
Cost of area A₂
C₂ = 0,05 * 48/x
C₂ = 2,4/x
Total cost C C = C₁ + C₂
C(x) = 0,15*π*x² + 24/x
Taking derivatives on both sides of the equation
C´(x) = 0,3**π*x - 24/x²
C´(x) = 0 0,3**π*x - 24/x² = 0
0,942 x³ = 24
x³ = 25,5
x = 2,94 ft and h = V/π*x² h = 24 /3,14* (2,94)²
h = 0,88 ft
C(min) = 0,15 * 3,14 * (2,94)² + 24/2,94
C(min) = 4,07 + 8,16
C(min) = 12,23 $
Answer:
a) Exterior Angle Theorem
b) x = 109°
Step-by-step explanation:
For a, you can thank the Exterior Angle Theorem. Since the angles of a triangle equal 180°, we can figure out what the third interior angle's measurement is, then subtract that from 180 to get the exterior angle's measure. Since the two angles labeled (64° and 45°) will make an obtuse angle, then the third interior is an acute angle. Add 64 and 45 to get the exterior angle's measurement of 109 degrees. That would mean the third interior angle's measurement would be 71 degrees. 64 + 45 + 71 = 180, so this is true.
(I had used the HSEAT to explain this.)